In computed tomography (CT), there are many instances where an object that is being scanned exceeds the detector's field of view. Projections acquired as such are referred to as “truncated scans.” A known technique for reconstructing volumes from scans such as those obtained using circular trajectory cone beam computed tomography (CBCT) with flat detectors involves the use of the Feldkamp-Davis-Kress (FDK) filtered backprojection (FBP) algorithm. The FDK FBP algorithm usually extends its projections (assumed non-truncated) using zero-padding for the purpose of ramp filtering. This works well for non-truncated projections because the left-right-most values of the scans are in fact zero after the log-scaling stage, and would indeed have been zero even further out, had the detector been larger. However, this is not the case with truncated projections and zero-padding introduces an unrealistic sharp edge that, in turn, introduces strong artifacts to the corresponding reconstructed image. Therefore further consideration is necessary to reconstruct volumes from truncated scans.
Conventional methods for performing CT reconstruction in conjunction with truncated scans view the problem as finding the missing parts of the projection. Such extrapolation-based methods involve specific algorithms, missing data extrapolation via linear prediction, iterative reconstruction, filteration backprojection, etc. However, such methods also force their extrapolated data to tend to zero within some finite number of samples. Such methods place assumptions on the object that was scanned. Moreover, such methods can also violate consistency conditions across projections: often, there does not exist an object such that untruncated scans of this object yield projections resembling the extrapolated data.
Furthermore, some methods do not lend themselves to a real-time streaming implementation, because processing one projection requires knowledge from one or more other projections that may not be available as yet. Some methods are designed for parallel beam scanning, so require rebinning and extra interpolation of the projection data. Other methods require that at least some of the projections should not have been subject be truncation: do not support the “interior problem” where all projections are truncated.
U.S. Pat. No. 4,674,045, entitled “Filter for Data Processing” describes a method to define the ramp filter in the spatial domain and to truncate the impulse response. However, such approach violates a fundamental filter requirement for FBP which is to null out the DC component of the frequency response. Further the corresponding frequency response has large ripple, which is undesirable.
In view of the aforementioned shortcomings associated with conventional approaches, there is a strong need in the art for a method and system for processing truncated projections beyond simply estimating the truncated data. There is a strong need in the art for a method and system in which artifacts may be avoided. There is a strong need for a method and system which lend themselves to real-time streaming implementation and which work efficiently for CT. Still further, there is a strong need in the art for a method and system that do not require data from other projections or prior knowledge of the object being reconstructed. There is a strong need for a method and system that work regardless of whether some or all projections are truncated. In addition, there is a strong need for a method and system that work for both symmetric and asymmetric detector configurations. In a symmetric detector configuration the iso-ray is intended to be coincident with the centroid of the detector, where as in an asymmetric detector configuration, the iso-ray is intended to be co-incident with a location that is offset from the centroid of the detector. For CBCT asymmetry due to a horizontal offset is the primary concern and can be specifically referred to as horizontal asymmetry.